A backstepping sliding mode control method for dual-motor driving servo system

Abstract

A double motor drive servo system back step sliding mode control method, the double motor drive servo system model with gear gap is established, the system state and control parameters are initialized; the gear gap function simulation is simulated by using the approximate dead zone function instead of the dead zone function; the improved double power approaching law is designed and simulated and compared with the double power approaching law; the controller is designed by using the back step control combined with the sliding mode control. The improved double power approaching law and the back step sliding mode control method designed in the application have good tracking control effect on the double motor servo system, can improve the control performance of the double motor servo system, and weaken the chattering of the input controller.

Description

Technical Field

[0001] This invention belongs to the field of servo system control technology, and relates to a backstepping sliding mode control method for a dual-motor driven servo system based on an improved double power-law approach, particularly for a control method for a dual-motor driven servo system with backlash. Background Technology

[0002] With the development of industrial automation, dual-motor drive servo systems are being used more and more widely in the field of industrial control. For dual-motor drive servo systems with high-precision control requirements, high-performance control is relatively difficult because the system is easily affected by nonlinear characteristics such as backlash nonlinearity, external disturbances, and parameter uncertainty.

[0003] Currently, researchers both domestically and internationally have proposed many control methods to address the aforementioned nonlinear problems. These include intelligent control, adaptive control, sliding mode control, backstepping control, and robust control.

[0004] Backlash nonlinearity is an unavoidable nonlinear characteristic of dual-motor driven servo systems, which degrades the system's control performance. To improve the tracking accuracy and response speed of dual-motor driven servo systems, many control methods have been proposed. Among these methods, sliding mode control has been widely studied due to its good robustness and disturbance rejection performance. However, chattering in sliding mode control limits its practical application. The reaching law sliding mode control method is one of the solutions to reduce chattering in sliding mode controllers. How to improve the reaching law to further weaken the chattering problem is of great research significance. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies and to mitigate the adverse effects of backlash nonlinearity on the dynamic and steady-state performance of dual-motor driven servo systems, this invention provides a backstepping sliding mode control method for dual-motor driven servo systems based on an improved double power-law approaching law. Considering the backlash of the system, an improved double power-law approaching law is designed to reduce the sliding mode chattering problem and ensure high-precision tracking control of the system even with backlash.

[0006] The technical solution proposed to solve the above-mentioned technical problems is as follows:

[0007] A method for backstepping sliding mode control of a dual-motor driven servo system includes the following steps:

[0008] Step 1: Establish a system model for the dual-motor driven servo system, and initialize the system state and control parameters. The process is as follows:

[0009] 1.1 The dynamic equations of the dual-motor driven servo system are expressed as follows:

[0010]

[0011] Among them, J i and J m Let θ be the moment of inertia of the driving wheel and the driven wheel, respectively. i and θ m These are the rotation angles of the driving wheel and the driven wheel, respectively. and These are the angular velocities of the driving wheel and the driven wheel, respectively. and b represents the angular acceleration of the driving wheel and the driven wheel, respectively. i and b m Let be the viscous friction coefficients of the driving and driven wheels, respectively, u(t) be the input torque of the system, and d be the viscous friction coefficients of the driving and driven wheels, respectively. i (t) represents the external disturbance, τ i (t) represents the torque transmitted between the driving wheel and the driven wheel, i = 1, 2;

[0012] 1.2, Considering motor backlash, the transmitted torque f(z i (t) is the dead-time function, f(z) i The form (t) can be written as:

[0013]

[0014] Where α is the tooth gap, z i (t)=θ i (t)-θ m Since the dead-zone function is not differentiable, controller design becomes difficult. To simplify the controller design, an approximate dead-zone function is chosen to replace the dead-zone function. The approximate dead-zone function is F(z). i The form (t) can be written as:

[0015]

[0016] Where r is a number greater than zero;

[0017] 1.3, Define new system state variables and rewrite equation (1) as follows:

[0018]

[0019] in, λ i =a2ρ i ;

[0020]

[0021] Step 2, improve the design of the double power-reaching law, the process is as follows:

[0022] 2.1, The improved form of the double power-reaching law is written as follows:

[0023]

[0024] Where b(s) represents the double power reaching law, It is an estimate of the uncertain terms;

[0025] 2.2, Filter s and b(s) as follows:

[0026]

[0027] Among them, s f b f These are the filtered values ​​of s and b(s), respectively; s f (0), b f (0) are the initial values ​​of s and b(s), respectively; l is the adjustment parameter;

[0028] From equations (5) and (6), we get:

[0029]

[0030] 2.3, The approach law after considering uncertainty Written in the form of:

[0031]

[0032] Step 3: Design of backstepping sliding mode control law based on improved double power-law approaching law.

[0033] Furthermore, the process of step 3 is as follows:

[0034] 3.1, Define the tracking error as e1 = x1 - y d ,but Where y d The system's reference position signal is used, and the sliding mode variable s1 is designed as follows:

[0035]

[0036] Where α1 is a constant;

[0037] The sliding mode variable s2 is designed as follows:

[0038] s2=x2-x 2d (10)

[0039] Among them, virtual control quantity

[0040] The sliding mode variable s3 is designed as follows:

[0041]

[0042] Among them, virtual control quantity

[0043] The sliding mode variable s4 is designed as follows:

[0044]

[0045] Among them, virtual control quantity

[0046] 3.2 The control law of the system is designed as follows:

[0047]

[0048] Where u2 is equal to u1, yes The estimated value;

[0049] 3.7, The Lyapunov function is defined as follows:

[0050]

[0051] in,

[0052] Differentiating equation (14) yields:

[0053]

[0054] 3.5 Substituting equations (5)-(14) into equation (15), we know that... The system is asymptotically stable.

[0055] This invention is based on the approaching law sliding mode control technology. It designs a backstepping sliding mode control method for a dual-motor driven servo system based on an improved double power approaching law. This method achieves high-precision control of a dual-motor driven servo system with backlash nonlinearity and unknown parameters and uncertainties, and reduces the input chattering problem of sliding mode control.

[0056] In recent years, dual-motor drives have been widely used in new energy vehicles. Dual-motor servo systems, which use two motors instead of a single motor, offer the following advantages: increased drive system power; improved control accuracy by effectively eliminating backlash in the transmission chain through appropriate measures; and reduced power requirements for each motor, thereby reducing design and cost limitations.

[0057] The technical concept of this invention is as follows: For dual-motor driven servo systems with backlash, backlash nonlinearity can adversely affect dynamic and steady-state performance. To improve the control performance of dual-motor driven servo systems, this invention designs a suitable backlash nonlinearity compensation method. First, the principle of dual-motor synchronous control is analyzed and a mathematical model of the system is established. Then, an approximate dead-zone function is used to replace the dead-zone function and serves as the system's backlash function. Next, an improved double-power-law approaching law with compensation terms for additional rates of change such as disturbances and noise is designed. Finally, a controller is designed using backstepping control combined with sliding mode control. This invention provides a method capable of compensating for additional rates of change, and the designed approach-law sliding mode control algorithm ensures that the servo system achieves better control performance while reducing the chattering problem of traditional sliding mode control.

[0058] The beneficial effects of this invention are: reducing chattering in sliding mode input and achieving high-performance tracking control of the dual-motor driven servo system. Attached Figure Description

[0059] Figure 1 This is a control flowchart of the present invention;

[0060] Figure 2 The reference signal is y d1 The tracking trajectory effect diagram at that time;

[0061] Figure 3 The reference signal is y d1 The tracking error effect diagram at that time;

[0062] Figure 4 The reference signal is y d1 The effect diagram of the control input u at that time;

[0063] Figure 5 The reference signal is y d2 The tracking trajectory effect diagram at that time;

[0064] Figure 6 The reference signal is y d2 The tracking error effect diagram at that time;

[0065] Figure 7 The reference signal is y d2 The effect diagram of the control input u during the time. Detailed Implementation

[0066] The invention will now be further described with reference to the accompanying drawings.

[0067] Reference Figures 1-7 A method for backstepping sliding mode control of a dual-motor driven servo system includes the following steps:

[0068] Step 1: Establish a system model for the dual-motor driven servo system, and initialize the system state and control parameters. The process is as follows:

[0069] 1.1 The dynamic equations of the dual-motor driven servo system are expressed as follows:

[0070]

[0071] Among them, J i and J m Let θ be the moment of inertia of the driving wheel and the driven wheel, respectively. i and θ m These are the rotation angles of the driving wheel and the driven wheel, respectively. and These are the angular velocities of the driving wheel and the driven wheel, respectively. and b represents the angular acceleration of the driving wheel and the driven wheel, respectively. i and b m Let be the viscous friction coefficients of the driving and driven wheels, respectively, u(t) be the input torque of the system, and d be the viscous friction coefficients of the driving and driven wheels, respectively. i (t) represents the external disturbance, τ i (t) represents the torque transmitted between the driving wheel and the driven wheel, i = 1, 2;

[0072] 1.2, Considering motor backlash, the transmitted torque f(z i (t) is the dead-time function, f(z) i The form (t) can be written as:

[0073]

[0074] Where α is the tooth gap, z i (t)=θ i (t)-θ m Since the dead-zone function is not differentiable, controller design becomes difficult. To simplify the controller design, an approximate dead-zone function is chosen to replace the dead-zone function. The approximate dead-zone function is F(z). i The form (t) can be written as:

[0075]

[0076] Where r is a number greater than zero;

[0077] 1.3, Define new system state variables and rewrite equation (1) as follows:

[0078]

[0079] in, λ i =a2ρi ;

[0080] Step 2, improve the design of the double power-reaching law, the process is as follows:

[0081] 2.1, The improved form of the double power-reaching law is written as follows:

[0082]

[0083] Where b(s) represents the double power reaching law, It is an estimate of the uncertain terms;

[0084] 2.2, Filter s and b(s) as follows:

[0085]

[0086] Among them, s f b f These are the filtered values ​​of s and b(s), respectively; s f (0), b f (0) are the initial values ​​of s and b(s), respectively; l is the adjustment parameter;

[0087] From equations (5) and (6), we get:

[0088]

[0089] 2.3, The approach law after considering uncertainty Written in the form of:

[0090]

[0091] Step 3, design the backstepping sliding mode control law based on the improved double power-reaching law, the process is as follows:

[0092] 3.1, Define the tracking error as e1 = x1 - y d ,but Where y d The system's reference position signal is used, and the sliding mode variable s1 is designed as follows:

[0093]

[0094] Where α1 is a constant;

[0095] The sliding mode variable s2 is designed as follows:

[0096] s2=x2-x 2d (10)

[0097] Among them, virtual control quantity

[0098] The sliding mode variable s3 is designed as follows:

[0099]

[0100] Among them, virtual control quantity

[0101] The sliding mode variable s4 is designed as follows:

[0102]

[0103] Among them, virtual control quantity

[0104] 3.2 The control law of the system is designed as follows:

[0105]

[0106] Where u2 is equal to u1, yes The estimated value;

[0107] 3.7, The Lyapunov function is defined as follows:

[0108]

[0109] in,

[0110] Differentiating equation (14) yields:

[0111]

[0112] 3.5 Substituting equations (5)-(14) into equation (15), we know that... The system is asymptotically stable.

[0113] To verify the control effect of the proposed method, a simulation experiment was conducted. The initial conditions for various parameters in the experiment were set as follows: system parameters α = 0.05, r = 10, J = 0.185, J... m =0.185, b=1.2, b m =1.3, b0=0.5, k=5, c=250; parameters of the double power reaching law: k1=10, k2=5, k3=7, k4=5, k5=7, k6=7, k7=7, k8=7. Initial conditions s f (0) = 0, b f (0) = 0. The reference signal y in the experiment... d Take respectively and

[0114] Figures 2-7 This is a simulation diagram of the control effect of a dual-motor driven servo system with backlash. Figure 2 and Figure 3 These represent reference signals y and y respectively. d1 The two figures show the tracking trajectory and tracking error at different times. They demonstrate that the proposed method can achieve good tracking performance, with the tracking error e reaching a very small range of [-2×10]. -3 2×10 -3 ]. Figure 4 The reference signal is y d1 The system input at that time. Through the improved double power-law approach, the chattering of the system input is relatively small. Figure 5 and Figure 6 The reference signal is y d2 The figure shows the tracking trajectory and tracking error at different times. It indicates that the system still has good tracking performance when the reference signal changes, and the maximum tracking error amplitude is -1×10. -3 . Figure 7 The reference signal is y d2 The system input at that time was reduced, and the input chattering was also reduced to an acceptable range. Simulation results show that the improved double-power-law approach control method proposed in this invention can reduce chattering and achieve high-performance tracking control of the system.

[0115] The above simulation experiments illustrate the effectiveness of the method designed in this invention. However, it is clear that this invention is not limited to the above examples, and various modifications can be made without departing from the basic spirit and scope of the invention. The improved double-power-law approach control method proposed in this invention can reduce chattering and achieve high-performance tracking control of the system.

Claims

1. A method for backstepping sliding mode control of a dual-motor driven servo system, characterized in that the method includes the following steps: Step 1: Establish a dual-motor driven servo system model and initialize the system state and control parameters. The process is as follows: 1.1 The dynamic equations of the dual-motor driven servo system are expressed as follows: （1）； in, and These are the moments of inertia of the driving wheel and the driven wheel, respectively. and These are the rotation angles of the driving wheel and the driven wheel, respectively. and These are the angular velocities of the driving wheel and the driven wheel, respectively. and These are the angular accelerations of the driving wheel and the driven wheel, respectively. and These are the coefficients of viscous friction of the driving and driven wheels, respectively. The input torque of the system, External disturbances For the torque transmitted between the driving wheel and the driven wheel, ; 1.2, Considering motor backlash, the transmitted torque , It is a dead-zone function. Written in the form of: （2）； in, It's a tooth gap. To simplify the controller design, an approximate dead-zone function is chosen instead of the actual dead-zone function. Written in the form of: （3）； in, It is a number greater than zero; 1.

3. Define new system state variables and rewrite equation (1) as follows: （4）； in, ; ; ; ; ; ; ； Step 2, improve the design of the double power-reaching law, the process is as follows: 2.1, The improved form of the double power-reaching law is written as follows: （5）； in, Represents the double power-to-nature law. It is an estimate of the uncertain term. , , , For the parameters of the double power-law approaching law, s For sliding mode variables; 2.2, will and Perform the filtering operation as follows: （6）； in, , They are and The filtered value; It refers to adjusting parameters; From equations (5) and (6), we get: （7）； 2.3, The approach law after considering uncertainty Written in the form of: （8）； Step 3: Design of backstepping sliding mode control law based on improved double power-law approaching law.

2. The method for backstepping sliding mode control of a dual-motor driven servo system as described in claim 1, characterized in that, The process of step 3 is as follows: 3.1, Define the tracking error as ,but ,in It is the system's reference position signal; design sliding mode variables. for: （9）； in, It is a constant; Design sliding mode variables for: （10）； Among them, virtual control quantity ; Design sliding mode variables for: （11）； Among them, virtual control quantity , , , , These are the parameters of the double power-law approach law; Design sliding mode variables for: （12）； Among them, virtual control quantity , , , , These are the parameters of the double power-law approach law; 3.2, The control law for the system is designed as follows: （13）； in, and equal, , , , These are the parameters of the double power-law approach law; 3.3, The Lyapunov function is defined as follows: （14）； in, , , ; Differentiating equation (14) yields: （15）； 3.4 Substituting equations (5)-(14) into equation (15), we know that... The system is asymptotically stable.

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